Yeah, it was just a guess based on context. Well in any case it's the identity function. I'd never heard "f maps A into A" meaning f is the identity function, and seemed f: A -> A would naturally be read as "f maps A into A" hence my original response.

Yeah, it was just a guess based on context. Well in any case it's the identity function. I'd never heard "f maps A into A" meaning f is the identity function, and seemed f: A -> A would naturally be read as "f maps A into A" hence my original response.

The word `into' is sometimes used to mean `injection' (much like `onto'). When there exists an injection, f, from A to B then it means you can find a copy of A in B, and so f maps A into B.

I would also presume, as did undefined, that 1A means the identity function ( or ) as this would be too easy an answer and noone would exclude any other bijection.